Can a musical have a half-life? “Miss Atomic Bomb” does, and it’s not quite long enough. Set against Nevada’s nuclear tests of the 1950s — specifically, the beauty pageants set up in their honor – the new musical starring Catherine Tate (“Doctor Who”) is a classic comic caper. Everyone gives everyone else the runaround: soldiers and showgirls, mobsters and spies. For all the fizz of its first half, however, the plot caves in on itself, never reaching the chain reaction of total farce. Its laughs come from revue skits and gags, and plenty of them, but, in the end, it’s relentless: a rictus smile of a musical.

Sixty-five miles from Las Vegas, out in the Nevada desert, the U.S. army spent the 1950’s splitting atoms. For enterprising Las Vegans, these detonations were just another tourist attraction. Restaurants held rooftop viewing parties. Hotels ran beauty pageants. In hindsight, these Miss Atomic contests became potent symbols of warped American values. There’s a sense of Rome burning, a “yee-haw” attitude that holds nothing sacred. The pageants eroticized death. They capitalized on it. They partied in its afterglow.

Theirs is a cartoon version of Vegas, but one that feels all too British, with its trigger-happy mobsters and motormouthed army officers. Under pressure from his Mafioso bosses, two-bit hotelier Lou Lubowitz (Simon Lipkin) needs to drum up bookings, and so cooks up the idea of a beauty pageant with his soldier brother Joey (Dean John-Wilson, the star of London’s upcoming outpost of “Aladdin”), on the run after ditching his desert post. En route to Vegas, Joey ran into a debt-ridden farmgirl, Candy (Florence Andrews) — exactly the sort of wholesome sweetheart who wins these things — and her fashion designer best friend Myrna (Tate).

To start, “Miss Atomic Bomb” looks like a sly subversion of musical theater’s cheer. The lyrics are laced with death, despite the upbeat score, so that when Candy and Myrna go in search of a better life, their vows “never to come home” take on an ominous tone. Gooey, cheesy love songs turn out to be hymns to cowardice and stubbornness. It’s sharp, fresh and ambitious.

But that early promise gradually disintegrates. Rather than driving at a particular point, “Miss Atomic Bomb” lets its various archetypes pair up and its plot plays out without surprises. Too often gags drive proceedings, so the musical swerves off for a song about sheep, and all the funny business — showgirl stereotypes and communist spies — is just that: funny business. The whole thing becomes increasingly distracted and disjointed (one plot point hinges on a rogue bar of soap), and so ends up compensating with strained comedy and showy numbers.

It doesn’t help that you don’t care about the characters, the product of wayward plotting. You care about the actors, but that’s different — more variety than musical theater. You appreciate Lipkin’s likeable clutz routine, as he fixes his best ‘you-bet-boss’ smile, despite a bullet in each foot, wincing as he tap dances in his tux, and Tate’s ability to sex everything up — even carrying on a sheep carcass — but you don’t remotely feel for them, even though everyone’s running from someone. Andrews has little to work with beyond a miraculous Cinderella transformation, and John-Wilson is dragged down by a series of tacky disguises as he hides from his superiors. The harder the show tries, the more testing it becomes.

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